( ii ) dimension characteristics

ii)    two dimensional network:  plane                               _________________________

geometry:  Any three noncollinear points, A, B, C, form a plane – the simplest polygon is a triangle featuring three vertices and three edges.   The association among these basic units is the transitive property of equivalence:  If A = B, and B = C, then A = C, creating a cyclical function.  Planes contain an infinite number of points and lines and extend unbounded in the direction of all lines.

 

transformations: rotation______________________________________________________

A rotation is a type of geometric transformation that maps any object, given by its individual components or coordinates, to another location in the same plane by turning it around a point.  In effect, this transformation is a spin – since the pre-image and the image are congruent, this transformation is an isometry.  A rotation can be accomplished by reflecting an object across 2 intersecting lines as a composition.

 

 

transformations: translation___________________________________________________

A translation is a type of geometric transformation that maps any object, given by its individual components or coordinates, to another location in the same plane by adding or subtracting units to the coordinates.  In effect, this transformation is a slide – since the pre-image and the image are congruent, this transformation is an isometry.  A translation can be accomplished by reflecting an object across 2 parallel lines as a composition.

 

 

ii)    complexity characteristics________________________________________________

key attribute:      function

affinities:            process                cognition

cog             wheel          sprocket

quantity                                                             periphery

parallax                crossover    juncture juxtapose          intersection

bearing                          heading                field

more           stability       equilibrium

shape                         polygon:  triangle quadrilateral penta-  hexa-  hepta-

speed          map

perimeter and area

oscillation,                 resonance,                    frequency

cycle  permutation

direction      spin,  turn,          revolve                                     orientation

period                      circuit                      transit

installation

slurry                   sequence              relay

waves: sine  cosine  tangent

periodic                phase shift

 

periodic table                                   predictable

diptych                                   fugue

organization

conic sections

mosaic                                            tessellations

                                             composite numbers        triangular numbers

                           platform

matrix filigree arabesque

task

ways and means

around                                                                    across

pattern process              induction

filter            amount bundle sieve

hold and                                                                     withhold

 

 

characteristics page

the map – second dimension

.